Joint Optimization of the Transmit Covariance and Relay Precoder in General Gaussian Amplify-and-Forward Relay Channels

The maximum data rate that can be achieved by the strictly causal full-duplex amplify-and-forward (AF) scheme in general Gaussian relay channels is achieved by Gaussian codebooks and can be cast as the solution of an optimization problem of the input transmit covariance and relay precoder. This prob...

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Vydáno v:	IEEE transactions on information theory Ročník 59; číslo 9; s. 5331 - 5351
Hlavní autoři:	Gohary, Ramy H., Yanikomeroglu, Halim
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 01.09.2013 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Access methods and protocols, osi model Applied sciences Asymptotic methods Codes Complexity theory Covariance matrices Exact sciences and technology Full-duplex AF relaying Information theory Information, signal and communications theory Joints KKT conditions MIMO Normal distribution Optimization Relays Schur basis Systems, networks and services of telecommunications Telecommunications Telecommunications and information theory Teleprocessing networks. Isdn Transmission and modulation (techniques and equipments) tridiagonal matrices Vectors Performance evaluation Relaying Relay Schur basis Interlacing KKT conditions Gaussian channel Coding circuit Transmission protocol Information rate Information transmission Optimization tridiagonal matrices Duplex process Full-duplex AF relaying Codebook Relay channel High power Covariance Routing protocols Causality Low-power electronics
ISSN:	0018-9448, 1557-9654
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Popis
Shrnutí:	The maximum data rate that can be achieved by the strictly causal full-duplex amplify-and-forward (AF) scheme in general Gaussian relay channels is achieved by Gaussian codebooks and can be cast as the solution of an optimization problem of the input transmit covariance and relay precoder. This problem possesses an intricate nonconvex structure and is hence difficult to solve. To circumvent this difficulty, the relay precoder is assumed to be given and then the Karush-Kuhn-Tucker conditions are used to obtain closed form expressions for the optimal input covariance corresponding to that precoder. These expressions are used to show that subdiagonal precoders suffice to attain the maximum achievable rate of the AF scheme at any source transmit power. In addition to significantly reducing the effort expended in searching for the optimal relay precoder, this observation enables us to find the optimal precoders at low and high source transmit powers. For asymptotically low transmit powers, the optimal relaying mechanism is shown to possess an interlacing structure, thereby resembling half-duplex operation. In contrast, for asymptotically high transmit powers, it is optimal for the relay to be silent. The asymptotic analysis enables us to develop an explicit formulation for a suboptimal precoder that, at intermediate source transmit powers, are shown numerically to outperform asymptotically optimal precoders.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2013.2266656